Earth oblateness error correction method for imaging earth sensors based on rough prior attitude information

Abstract

The present invention discloses a method for correcting Earth flattening errors in an imaging Earth sensor based on rough prior attitude information. The method first requires the attitude control system to periodically input current attitude data to the Earth sensor and perform kinematic recursion within the Earth sensor to obtain rough prior attitude information at the moment the Earth sensor takes an image. This rough prior attitude information is then used to transform the horizon vector from a slightly flattened Earth ellipsoid at the poles to a uniform sphere, achieving an early correction for Earth flattening. Finally, spatial circle fitting is used to achieve high-precision calculation of the Earth's center of gravity (CGM). This method does not rely on high-precision prior attitude information, has low requirements for external input and internal computing power, and is suitable for standalone Earth sensor designs. It can fully eliminate the effects of Earth flattening on the Earth sensor and effectively improve the accuracy of CGM calculations.

Description

Technical Field

[0001] The present invention relates to the field of algorithm design of earth sensors, and in particular to a method for correcting measurement errors of earth sensors caused by the earth's oblateness. Background Art

[0002] The Earth sensor is a traditional and reliable attitude sensor for spacecraft. It detects the Earth's horizon in infrared, visible, and ultraviolet spectra, providing a stable and accurate geocentric vector. Combined with other sensors, including sun sensors, magnetometers, and star trackers, it enables autonomous attitude and orbit determination for spacecraft. Further improvements in the Earth sensor's accuracy are affected by factors such as Earth limb positioning accuracy, the effect of Earth's oblateness, seasonal variations in Earth's radiance, and mounting matrix bias and drift. Errors caused by Earth's oblateness are particularly significant.

[0003] The influence of Earth's oblateness is often overlooked in Earth sensor design because it is very small, only about 1 / 298. However, cross-validation of on-orbit data from Earth sensors and star sensors indicates that observations from on-orbit infrared Earth sensors contain periodic errors related to spacecraft position and attitude. The Earth sensor's periodic errors are significantly greater than its short-term noise, primarily due to the neglected influence of Earth's oblateness. In applications of joint orbit determination using star and Earth sensors, polynomial fitting can be used to suppress Earth sensor noise. While polynomial fitting can partially mitigate these errors, the parameters must be regularly updated and require the assistance of higher-precision sensors, such as star sensors. A more rational approach is to consider Earth sensor oblateness in the Earth sensor's algorithm design and make appropriate corrections to fundamentally address the problem.

[0004] Traditional Earth sensors offer a number of excellent methods for correcting for the effects of Earth's oblateness. For example, using a priori known position or attitude information of the spacecraft to iteratively correct the horizon crossing points, thereby resolving the geocenter vector with higher accuracy. However, imaging Earth sensors detect hundreds of times more horizon points than horizon crossing points, resulting in an unacceptable computational workload.

[0005] In their invention patent, "A Method for Correcting Earth Flattening in an Imaging Earth Sensor," Hao Yuncai and others from the Beijing Institute of Control Engineering proposed a method for correcting Earth flattening errors based on secondary calculations. This method requires two steps. The first step is to calculate a rough geocentric vector that disregards Earth flattening and transmit it to the attitude and orbit control system. The second step is to use the attitude and orbit control system to calculate the current attitude information based on the rough geocentric vector. The Earth sensor then corrects each horizon vector based on the current spacecraft position and attitude information provided by the attitude and orbit control system, and then recalculates the geocentric vector that accounts for Earth flattening. This method relies on deep coupling between the spacecraft attitude and orbit control system and the Earth sensor, resulting in complex system design and significant limitations. Furthermore, the method requires secondary interaction and calculations, resulting in poor real-time performance and making it unsuitable for stand-alone designs of modern Earth sensors.

[0006] In their invention patent, "Earth Flattening Compensation Method for Imaging Earth Sensors Based on Trigonometric Function Fitting," Guan Lexin et al. from the Beijing Institute of Control Engineering propose a method for correcting Earth flattening errors based on trigonometric function fitting. This method compares the geocentric vector calculated when the Earth is a standard sphere with the geocentric vector calculated when the Earth is an ellipsoid to determine the theoretical deviation caused by Earth flattening errors. This deviation is then subjected to trigonometric function fitting to achieve Earth flattening correction. This method is essentially the polynomial fitting algorithm mentioned above, but uses the theoretical error calculated under ideal conditions as input. However, this algorithm considers the ideal case, where the spacecraft is pointing toward the Earth and the Earth sensor captures the entire horizon. However, when the spacecraft is mis-pointing, particularly when the angle between the Earth's center vector and the Earth sensor is large, the horizon edge may be missing. In this case, the trigonometric function compensation value will differ significantly from the actual Earth flattening error introduced by the Earth sensor, resulting in poor correction. In addition, the Earth's oblateness error is related to the spacecraft's orbital altitude and latitude. Therefore, when the Earth sensor is applied to spacecraft in different orbits, or when the spacecraft orbit shifts, the original trigonometric function fitting value is no longer applicable and the parameters need to be continuously updated. Summary of the Invention

[0007] The present invention provides a method for correcting the Earth flattening error of an imaging Earth sensor based on rough prior attitude information. The method can effectively eliminate the Earth sensor measurement error caused by the Earth flattening, effectively improve the Earth sensor's geocentric vector measurement accuracy, and provide a solid foundation for the application of Earth sensors in tasks such as spacecraft attitude determination and orbit determination.

[0008] The object of the present invention is achieved through the following technical solutions:

[0009] A method for correcting earth flattening errors of an imaging earth sensor based on rough prior attitude information comprises the following steps:

[0010] 1) The spacecraft's attitude and orbit control system sends the spacecraft's current attitude information to the Earth sensor during each spacecraft attitude determination cycle. The Earth sensor uses the spacecraft's current attitude information to perform kinematic recursion, thereby calculating the rough prior attitude information of the Earth sensor at each photo-taking moment.

[0011] 2) The earth sensor uses the rough prior attitude information to transform all measured earth horizon vectors, transforming the horizon vectors on the earth ellipsoid taking into account the flattening into the horizon vectors on a uniform sphere, thereby achieving early correction for the effect of the earth's flattening;

[0012] 3) The transformed horizon vector is solved by using a least squares algorithm to obtain the transformed geocentric vector, and then the transformed geocentric vector is inversely transformed to obtain the geocentric vector that eliminates the effect of the earth's flattening.

[0013] In the above technical solution, further, the step 1) is specifically:

[0014] The Earth's center of mass O P As the origin, the center of mass of the earth O P The direction pointing to the intersection of the prime meridian and the equator is X P Axis, with the Earth's center of mass O P The direction pointing to the North Pole is Z P Axis, Y P Perpendicular to X P Axis and Z P Axis, establish the Earth-centered Earth-fixed coordinate system P; with the optical center of the Earth sensor O C As the origin, the row direction of the image sensor of the earth sensor is X C Axis, the column direction of the image sensor of the earth sensor is Y C Axis, Z C Perpendicular to X C Axis and Y C Axis, establish the earth sensor camera coordinate system C;

[0015] In each spacecraft attitude determination cycle, the attitude orbit control system provides the Earth sensor with the attitude transformation matrix from the Earth sensor camera coordinate system C to the Earth-centered Earth-fixed coordinate system P at time t0: And the angular velocity of the spacecraft in the Earth sensor camera coordinate system C for In X C The axis weight, for In YC The axis weight, for In Z C The axis's component;

[0016] A timer is started inside the earth sensor to measure the time interval Δt from time t0 to the moment when the earth sensor camera takes the photo exposure center; then the rough prior attitude information of the earth sensor camera at time t0+Δt can be obtained by kinematic recursion:

[0017]

[0018] in, is the attitude matrix, which represents the rough prior attitude information of the earth sensor camera at time t0+Δt; Represents the rotation matrix caused by the rotation of the spacecraft in the time interval Δt; considering that the time interval Δt is shorter than a spacecraft attitude determination cycle, it can be approximated by using the first-order Taylor expansion and ignoring the higher-order terms That is, the expression is as follows:

[0019]

[0020] Among them I 3×3 Represents the identity matrix with 3 rows and 3 columns;

[0021] During the next spacecraft attitude determination cycle, the Earth sensor refreshes and At the same time, the timer is restarted from the new time t0.

[0022] Furthermore, the step 2) is specifically as follows:

[0023] For each horizon vector in the earth sensor camera coordinate system C measured by the earth sensor Apply the Earth oblateness correction transformation to it:

[0024]

[0025] in is the flattening-corrected horizon vector, yes The inverse matrix of , Q is the earth flattening scaling matrix:

[0026]

[0027] where R e represents the average radius of the Earth, a represents the equatorial radius of the Earth, and c represents the polar radius of the Earth.

[0028] The specific principle of the Earth flattening correction transformation is: for each measured horizon vector First of all, Left multiplication The horizon vector is transformed from the Earth sensor camera coordinate system C to the Earth-centered Earth-fixed coordinate system P; then Multiply Q on the left to scale the Earth-centered Earth-fixed coordinate system P. Based on the Earth's equatorial radius and polar radius, it is uniformly scaled to the Earth's average radius R. e , thus transforming the earth from a slightly flattened ellipsoid at the poles into a uniform sphere; finally Left multiplication Convert it to the flattening-corrected camera coordinate system to get the flattening-corrected horizon vector

[0029] Furthermore, the step 3) is specifically as follows:

[0030] Considering that the horizon vector after flattening correction is on a uniform sphere, then these horizon vectors after flattening correction are Scaled to unit vector h i After that, an ideal space circle will be formed, so the following measurement equation can be constructed:

[0031] Hχ=y (14)

[0032] in:

[0033] H=[h1 h2 … h i … h n ] T (15)

[0034] y=1 n×1 (16)

[0035] χ represents the geocentric vector in the camera coordinate system after flattening correction, 1 n×1 Represents a matrix with n rows and 1 column all set to 1. The least squares method can be used to solve it:

[0036] χ=(H T H) -1 H T y (17)

[0037] The geocentric vector χ after flattening correction is inversely transformed and scaled to a unit vector to obtain the geocentric vector that eliminates the effect of the earth's flattening. The specific calculation process is as follows:

[0038]

[0039] The inventive principle of the present invention is:

[0040] The present invention proposes a method for correcting Earth flattening errors in imaging Earth sensors based on rough prior attitude information. This method first obtains rough prior attitude information of the Earth sensor at the moment the image is taken, using periodic input of current attitude data and internal kinematic recursion. This rough prior attitude information is then used to transform the Earth from a slightly flattened ellipsoid at the poles into a uniform sphere, greatly simplifying the problem. Finally, a least-squares algorithm is used to achieve high-precision calculation of the Earth's center-of-center vector. This correction method does not rely on high-precision prior attitude information, has low requirements for external input and internal computing power, and is suitable for stand-alone Earth sensor designs. It can fully eliminate the effects of Earth flattening on the Earth sensor, effectively improving the accuracy of Earth's center-of-center vector calculations and providing a solid foundation for the application of Earth sensors in spacecraft attitude and orbit determination.

[0041] Compared with the prior art, the present invention has the following beneficial effects:

[0042] 1. This invention addresses the issue of inconsistency between the attitude determination frequency of the spacecraft attitude and orbit control system and the photography frequency of the Earth sensor. It utilizes periodic communication interaction and kinematic recursion to obtain rough prior attitude information from the Earth sensor, thus reducing the burden on the spacecraft attitude and orbit control system.

[0043] 2. The present invention eliminates the error caused by the earth's flattening in the earth sensor as much as possible by making full use of the rough prior attitude information, thereby greatly improving the measurement accuracy of the earth's center vector of the earth sensor.

[0044] 3. The present invention corrects errors caused by the Earth's flattening at different orbital altitudes, different latitudes, and different attitudes, especially when the angle between the Earth's center vector and the horizon edge is large, by transforming and correcting each measured horizon vector. This is a more universal and efficient method. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] The above and / or additional aspects and advantages of the present invention will become apparent and understood from the following description of the embodiments with reference to the accompanying drawings, in which:

[0046] Figure 1 Schematic diagram of obtaining prior rough attitude information for earth sensors;

[0047] Figure 2 Schematic diagram of the process of taking pictures of the Earth by an Earth sensor;

[0048] Figure 3 The error distribution of the Earth sensor's geocentric vector measurement at different latitudes before and after flattening correction is shown in the figure. RMSE stands for root mean square error.

[0049] Figure 4The error distribution of the Earth sensor's geocentric vector measurement before and after the flattening correction at different orbital altitudes is shown in Figure 2.

[0050] Figure 5 The error distribution of the earth sensor's geocentric vector measurement before and after flattening correction at different geocentric vector angles is shown in Figure 2. DETAILED DESCRIPTION

[0051] The present invention provides a method for correcting earth flattening errors of an imaging earth sensor based on rough prior attitude information, and the implementation steps are as follows:

[0052] 1) The spacecraft's attitude and orbit control system sends the spacecraft's current attitude information to the Earth sensor during each spacecraft attitude determination cycle. The Earth sensor uses the spacecraft's current attitude information to perform kinematic recursion, thereby calculating the rough prior attitude information of the Earth sensor at each photo-taking moment (such as Figure 1 );

[0053] 2) The earth sensor uses the rough prior attitude information to transform all measured earth horizon vectors, transforming the horizon vectors on the earth ellipsoid taking into account the flattening into the horizon vectors on a uniform sphere, thereby achieving early correction for the effect of the earth's flattening;

[0054] 3) The transformed horizon vector is solved by using a least squares algorithm to obtain the transformed geocentric vector, and then the transformed geocentric vector is inversely transformed to obtain the geocentric vector that eliminates the effect of the earth's flattening.

[0055] The step 1) is specifically as follows:

[0056] like Figure 2 As shown, the Earth's center of mass O P As the origin, the center of mass of the earth O P The direction pointing to the intersection of the prime meridian and the equator is X P Axis, with the Earth's center of mass O P The direction pointing to the North Pole is Z P Axis, Y P Perpendicular to X P Axis and Z P Axis, establish the Earth-centered Earth-fixed coordinate system P; with the optical center of the Earth sensor O C As the origin, the row direction of the image sensor of the earth sensor is X C Axis, the column direction of the image sensor of the earth sensor is Y C Axis, Z C Perpendicular to X C Axis and Y C Axis, establish the earth sensor camera coordinate system C;

[0057] In each spacecraft attitude determination cycle, the attitude orbit control system provides the Earth sensor with the attitude transformation matrix from the Earth sensor camera coordinate system C to the Earth-centered Earth-fixed coordinate system P at time t0: And the angular velocity of the spacecraft in the Earth sensor camera coordinate system C for In X C The axis weight, for In Y C The axis components, for In Z C The axis's weight;

[0058] A timer is started inside the earth sensor to measure the time interval Δt from time t0 to the moment when the earth sensor camera takes the photo exposure center; then the rough prior attitude information of the earth sensor camera at time t0+Δt can be obtained by kinematic recursion:

[0059]

[0060] in, is the attitude matrix, which represents the rough prior attitude information of the earth sensor camera at time t0+Δt; Represents the rotation matrix caused by the rotation of the spacecraft in the time interval Δt; considering that the time interval Δt is shorter than a spacecraft attitude determination cycle, it can be approximated by using the first-order Taylor expansion and ignoring the higher-order terms That is, the expression is as follows:

[0061]

[0062] Among them I 3×3 Represents the identity matrix with 3 rows and 3 columns;

[0063] During the next spacecraft attitude determination cycle, the Earth sensor refreshes and At the same time, the timer is restarted from the new time t0.

[0064] The step 2) is specifically as follows:

[0065] For each horizon vector in the earth sensor camera coordinate system C measured by the earth sensor Apply the Earth oblateness correction transformation to it:

[0066]

[0067] in is the flattening-corrected horizon vector, yes The inverse matrix of , Q is the earth flattening scaling matrix:

[0068]

[0069] where R e represents the average radius of the Earth, a represents the equatorial radius of the Earth, and c represents the polar radius of the Earth.

[0070] The specific principle of the Earth flattening correction transformation is: for each measured horizon vector First of all, Left multiplication The horizon vector is transformed from the Earth sensor camera coordinate system C to the Earth-centered Earth-fixed coordinate system P; then Multiply Q on the left to scale the Earth-centered Earth-fixed coordinate system P. Based on the Earth's equatorial radius and polar radius, it is uniformly scaled to the Earth's average radius R. e , thus transforming the earth from a slightly flattened ellipsoid at the poles into a uniform sphere; finally Left multiplication Convert it to the flattening-corrected camera coordinate system to get the flattening-corrected horizon vector

[0071] The step 3) is specifically as follows:

[0072] Considering that the horizon vector after flattening correction is on a uniform sphere, then these horizon vectors after flattening correction are Scaled to unit vector h i After that, an ideal space circle will be formed, so the following measurement equation can be constructed:

[0073] Hχ=y (23)

[0074] in:

[0075] H=[h1 h2…h i …h n ] T (twenty four)

[0076] y=1 n×1 (25)

[0077] χ represents the geocentric vector in the camera coordinate system after flattening correction, 1 n×1 Represents a matrix with n rows and 1 column all set to 1. The least squares method can be used to solve it:

[0078] χ=(H T H) -1 H T y (26)

[0079] The geocentric vector χ after flattening correction is inversely transformed and scaled to a unit vector to obtain the geocentric vector that eliminates the effect of the earth's flattening. The specific calculation process is as follows:

[0080]

[0081] Example:

[0082] In order to more clearly demonstrate the advantages of this method, the on-orbit operation process of the earth sensor is simulated, and the results of applying the flattening correction algorithm provided by the present invention are compared with the results of the algorithm that directly solves the geocentric vector without considering the earth's flattening.

[0083] Assume that the Earth sensor uses an infrared fisheye camera that follows the equidistant projection principle, with a 180-degree circular field of view and an image sensor resolution of 512×512 pixels. The field of view is inscribed in the image sensor, and the horizon edge positioning errors in the row and column directions are both Gaussian distribution errors with a standard deviation of 0.5 pixels. The spacecraft's attitude and orbit control system sends the Earth sensor the spacecraft's current attitude information every second. The three-axis errors of the rough prior attitude information obtained by the Earth sensor relative to the true attitude information are all Gaussian distribution errors with a standard deviation of 1 degree. The average radius of the Earth, R e The equatorial radius is 6377.83 km, and the polar radius is 6356.91 km.

[0084] Figure 3 Figure 2 shows the distribution of the Earth sensor's geocentric vector measurement error at different latitudes, before and after oblateness correction. The spacecraft altitude is set at 500 km, the Earth sensor is facing the Earth's center, and the latitude varies from 0 to 90 degrees. It can be seen that before oblateness correction, the Earth sensor exhibits an error that varies with latitude. This error is maximum at 45 degrees, with the geocentric vector error reaching 0.16 degrees. The proposed oblateness correction algorithm effectively eliminates this error at all latitudes.

[0085] Figure 4 Figure 2 shows the distribution of the Earth sensor's geocentric vector measurement error at different orbital altitudes, before and after oblateness correction. The spacecraft latitude is set to 45 degrees, the Earth sensor is facing the Earth's center, and the spacecraft altitude varies from 300 km to 40,000 km. It can be seen that before oblateness correction, the Earth sensor exhibits an error that varies with orbital altitude. This error decreases with increasing orbital altitude. The proposed oblateness correction algorithm effectively eliminates this error at all orbital altitudes.

[0086] Figure 5Figure 2 shows the distribution of the Earth sensor's geocentric vector measurement error before and after flattening correction for different geocentric vector angles. The spacecraft latitude is set to 45 degrees, the spacecraft altitude is set to 500 km, and the geocentric vector angle measured by the Earth sensor varies from 0 degrees to 100 degrees. It can be seen that before flattening correction, the Earth sensor has an error that varies with the geocentric vector angle. The proposed flattening correction algorithm effectively eliminates this error at different geocentric vector angles.

Claims

1. A method for correcting earth flattening errors of an imaging earth sensor based on rough prior attitude information, characterized in that: The steps include: 1) The spacecraft's attitude and orbit control system sends the spacecraft's current attitude information to the Earth sensor during each spacecraft attitude determination cycle. The Earth sensor uses the spacecraft's current attitude information to perform kinematic recursion, thereby calculating the rough prior attitude information of the Earth sensor at each photo-taking moment. 2) The earth sensor uses the rough prior attitude information to transform all measured earth horizon vectors, transforming the horizon vectors on the earth ellipsoid taking into account the flattening into the horizon vectors on a uniform sphere, thereby achieving early correction for the effect of the earth's flattening; 3) The transformed horizon vector is solved by using a least squares algorithm to obtain the transformed geocentric vector, and then the transformed geocentric vector is inversely transformed to obtain the geocentric vector that eliminates the effect of the earth's flattening.

2. The method for correcting earth flattening error of an imaging earth sensor based on rough prior attitude information according to claim 1, characterized in that: The step 1) is specifically as follows: The Earth's center of mass O P As the origin, the center of mass of the earth O P The direction pointing to the intersection of the prime meridian and the equator is X P Axis, with the Earth's center of mass O P The direction pointing to the North Pole is Z P Axis, Y P Perpendicular to X P Axis and Z P Axis, establish the Earth-centered Earth-fixed coordinate system P; with the optical center of the Earth sensor O C As the origin, the row direction of the image sensor of the earth sensor is X C Axis, the column direction of the image sensor of the earth sensor is Y C Axis, Z C Perpendicular to X C Axis and Y C Axis, establish the earth sensor camera coordinate system C; In each spacecraft attitude determination cycle, the attitude orbit control system provides the Earth sensor with the attitude transformation matrix from the Earth sensor camera coordinate system C to the Earth-centered Earth-fixed coordinate system P at time t0: And the angular velocity of the spacecraft in the Earth sensor camera coordinate system C for In X C The axis weight, for In Y C The axis weight, for In Z C The axis's weight; The timer is started inside the earth sensor to measure the time interval Δt from time t0 to the moment when the earth sensor camera takes the photo exposure center; then the rough prior attitude information of the earth sensor camera at time t0+Δt can be obtained by kinematic recursion: in, is the attitude matrix, which represents the rough prior attitude information of the earth sensor camera at time t0+Δt; Represents the rotation matrix caused by the rotation of the spacecraft in the time interval Δt; considering that the time interval Δt is shorter than a spacecraft attitude determination cycle, it can be approximated by using the first-order Taylor expansion and ignoring the higher-order terms That is, the expression is as follows: Among them I 3×3 Represents the identity matrix with 3 rows and 3 columns; During the next spacecraft attitude determination cycle, the Earth sensor refreshes and At the same time, the timer is restarted from the new time t0.

3. The method for correcting earth flattening error of an imaging earth sensor based on rough prior attitude information according to claim 2, characterized in that: The step 2) is specifically as follows: For each horizon vector in the earth sensor camera coordinate system C measured by the earth sensor Apply the Earth oblateness correction transformation to it: in is the flattening-corrected horizon vector, yes The inverse matrix of , Q is the earth flattening scaling matrix: where R e represents the average radius of the Earth, a represents the equatorial radius of the Earth, and c represents the polar radius of the Earth.

4. The method for correcting earth flattening error of an imaging earth sensor based on rough prior attitude information according to claim 3, characterized in that: The step 3) is specifically as follows: These flattening-corrected horizon vectors Scaled to unit vector h i Then, the following measurement equation is constructed: Hχ=y (5) in: H=[h1 h2…h i …h n ] T (6) y＝1 n×1 (7) χ represents the geocentric vector after flattening correction, 1 n×1 Represents a matrix with n rows and 1 column all set to 1; the least squares method can be used to solve it: χ=(H T H) -1 H T y (8) The geocentric vector χ after flattening correction is inversely transformed and scaled to a unit vector to obtain the geocentric vector that eliminates the effect of the earth's flattening. The specific calculation process is as follows:

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